Super (a, d)-Edge Antimagic Total Labeling of Connected Ferris Wheel Graph

  • Djoni Budi Sumarno Jurusan Matematika, Fakultas MIPA, Universitas Jember Jln. Kalimantan 37, Jember 68121
  • D Dafik
  • Kiswara Agung Santoso

Abstract

Let G be a simple graph of order p and size q. Graph G is called an (a,d)-edge-antimagic totalifthereexistabijectionf :V(G)∪E(G)→{1,2,...,p+q}suchthattheedge-weights,w(uv)= f(u)+f(v)+f(uv); u, v ∈ V (G), uv ∈ E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a, d)-edge antimagic total properties of connected of Ferris Wheel F Wm,n by using deductive axiomatic method. The results of this research are a lemma or theorem. The new theorems show that a connected ferris wheel graphs admit a super (a, d)-edge antimagic total labeling for d = 0, 1, 2. It can be concluded that the result of this research has covered all feasible d.

Key Words : (a, d)-edge antimagic vertex labeling, super (a, d)-edge antimagic total labeling, Ferris Wheel graph FWm,n.

 

Published
2015-04-03
How to Cite
SUMARNO, Djoni Budi; DAFIK, D; SANTOSO, Kiswara Agung. Super (a, d)-Edge Antimagic Total Labeling of Connected Ferris Wheel Graph. Jurnal ILMU DASAR, [S.l.], v. 15, n. 2, p. 123-130, apr. 2015. ISSN 2442-5613. Available at: <https://jurnal.unej.ac.id/index.php/JID/article/view/1051>. Date accessed: 02 oct. 2022. doi: https://doi.org/10.19184/jid.v15i2.1051.
Section
General